Fabregas picked out a more reliable finisher in Costa with another inch-perfect pass, the striker slotting calmly through Brad Guzan's legs to equal his best league tally with his 20th of the season.
It leaves Conte's side with a clean bill of health as they bid to secure the double in the Italian's first season in England.
Former Chelsea winger Clive Walker believes Middlesbrough let their fans down with their inept performance at Stamford Bridge against the Blues on Monday night. They deserve to be where they are.
"We've had 36 games with two to go and it's been a tough season", added the manager.
The Blues have the chance to claim their second league title in three seasons when they face West Brom on Friday.
Tottenham Hotspur's defeat at West Ham United last week, coupled with Chelsea's defeat of Middlesbrough on Monday, significantly eased the pressure during the run-in. Data company Opta are the official media data partner of the Premier League this season, and they had some good news for Fabregas the morning after the match. "They will want to play a top game against us". "Over the years we've had good games against them and we've had a few good results at The Hawthorns, so we'll be turning up confident and trying to win the game", McAuley said. We're still doing the right things, there's no complacency.
Cesc Fabregas urged Chelsea to wrap up the Premier League title on Friday after the leaders moved within touching distance of the silverware thanks to the Spaniard's inspired display.
The Spain global began this season's campaign outside the Chelsea first team and Fabregas acknowledged it was hard to get used to not being an integral part of Antonio Conte's plans.
The Baggies need five more points to eclipse the club's highest tally of 49 in a Premier League season, set in 2012-13. "It's not easy and people told me I'm not the type of player for Antonio and that I should leave, but I like challenges".
Chelsea manager Antonio Conte has admitted that his side's 3-0 defeat to Arsenal earlier in the season was a pivotal moment for him at the club and in this season's title race.
"We have to gain more points to finish strongly, then everything moving forward will be aimed at getting back into the Premier League as soon as possible".
With their drop to the Championship, it may make a deal easier for West Brom to make after the defender has had a taste of the top-flight.style="text-align: center;"